title: Angiogenesis inhibition and tumor-immune interactions with chemotherapy by a control set-valued method.
abstract: In this paper, two cancer therapies are investigated through their mathematical models. Namely, angiogenesis inhibition (P. Hahndfeldt, D. Panigrahy, J. Folkman, L. Hlatky, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy, Cancer Res. 59, 1999, 4770-4775) and tumor-immune interactions with chemotherapy (L. De Pillis, W. Gu, K.R. Fister, T. Head, K. Maples, A. Murugan, T. Neal, K. Yoshida, Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls. Math. Biosci. 209 (1), 2007, 292-315). The feedback protocols are determined by using a control set-valued method whose mathematical foundations are stated in (K. Kassara, A unified set-valued approach to control immunotherapy, SIAM J. Contr. Optim. 48 (2), 2009, 909-924), and which is demonstrated to be well suited for cancer control.
authors.affiliation: Systems and Control Group, University Hassan II, P.O. Box 5366, Casablanca, Morocco. kassarak@ams.org
authors.forename: K
authors.initials: K
authors.lastname: Kassara
authors.forename: A
authors.initials: A
authors.lastname: Moustafid
mesh_terms: D020533:Angiogenesis Inhibitors / Q000627:therapeutic use*; D000970:Antineoplastic Agents / Q000627:therapeutic use*; D003198:Computer Simulation; D006801:Humans; D018448:Models, Immunological; D009369:Neoplasms / Q000098:blood supply / Q000188:drug therapy* / Q000276:immunology; D009389:Neovascularization, Pathologic / Q000188:drug therapy / Q000276:immunology; D013269:Stochastic Processes
chemical_list: D020533:Angiogenesis Inhibitors; D000970:Antineoplastic Agents